Theory and Decision

, Volume 83, Issue 4, pp 469–498 | Cite as

On the characterization of weighted simple games

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Abstract

This paper has a twofold scope. The first one is to clarify and put in evidence the isomorphic character of two theories developed in quite different fields: on one side, threshold logic, on the other side, simple games. One of the main purposes in both theories is to determine when a simple game is representable as a weighted game, which allows a very compact and easily comprehensible representation. Deep results were found in threshold logic in the sixties and seventies for this problem. However, game theory has taken the lead and some new results have been obtained for the problem in the past two decades. The second and main goal of this paper is to provide some new results on this problem and propose several open questions and conjectures for future research. The results we obtain depend on two significant parameters of the game: the number of types of equivalent players and the number of types of shift-minimal winning coalitions.

Keywords

Simple games Weighted games Characterization of weighted games Trade robustness Invariant-trade robustness 

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Copyright information

© Springer Science+Business Media New York 2017

Authors and Affiliations

  1. 1.Department of MathematicsUniversitat Politècnica de Catalunya (Campus Manresa)ManresaSpain
  2. 2.CirprotecTerrassaSpain
  3. 3.Department of MathematicsUniversity of BayreuthBayreuthGermany

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